Navelpluis, I will give you a Garchomp, which must be called Poseidon (who on his days off from being god of the seas was also god of earthquakes). This is hugely ironic, because this Garchomp will never learn Earthquake, and in fact will never learn any move, apart from by level-up, apart from Surf (which is mandatory), to show that he is being diligent and keeping to his primary job of organising the seas. However, to show that a Garchomp without Earthquake, Outrage, Draco Meteor, Swords Dance, Fire Fang (just to name a few) can still be good, it must solo the Ice-type gym, and then Cynthia's Garchomp. Enjoy.
Navel, i'm gonna give you a slightly different challenge: You get a MEP! But it's not just any old MEP. This one comes with a free Shinx! Here's the deal: You have to catch a Shinx on the first route you encounter one, and must have one by the time you reach Floaroma Town. Call it Fuego. It has no restrictions....Unfortunately, Dialga does not like this Shinx and kills it during your Battle at the Spear Pillar. Therefore, you must immediately release (or box, if you don't like releasing) Fuego after Spear Pillar. It will be replaced with a MEP, which you will catch under Lv. 15. This MEP may only battle Trainers or you may fight wild pokemon on Iron Island with it. Also, it may not hold Exp. Share under any circumstances. Call it "DamnYouA1!".
Oh, and if you don't know what a MEP is, it's a prize we give to all newcomers to this thread. A Mono Electric Pachirisu, i.e. a Pachirisu that can only use electric attacks in battle.
I give you KrowMasta the Murkrow. This guy is just cocky. He really thinks he's the best murkrow ever and therefore he thinks he doesn't need to evolve. You're his trainer so you'll accept his choice. He also thinks he doesn't even need to fly to be the best and he won't even flap his wings so no flying-type moves. However, on the battle against Byron, KrowMasta realizes he couldn't even scratch his opponents and therefore he needs to rest and rethink his lifestyle. After you win the 7th badge he realizes he's ready to battle again and he'll do the best he can to help his trainer except changing who he is.
Navel, take Turtwig as your starter. Its shell is really goddamn heavy, so SR for a Relaxed nature. It can't learn any moves with a BP of 100 or higher because of how chillin' it is.
Navel, catch a Ponyta. This Ponyta is not an admirer of the fast lifestyle, so SR until you get one with a minus Speed nature. It can also never learn Agility. It can only evolve after it solos 5 gym leader pokemon.
Navel, if you still have a spot, you get the Riolu you receive from Riley. It must be Lucario before your battle with Dialga. Once it evolves, it becomes an Odd/Even Lucario! If it's an Odd level, it can only fight wild Pokemon (unless you have no other choice). If it's an Even level, it can only fight in a trainer battle (if it is your only Pokemon and you fight a wild Pokemon, you must run away). If it levels up during a trainer battle, you must immediately withdraw it from combat if possible. You cannot use an Exp.Share on it.